Tagged Questions

Questions on optimizing Mathematica code for higher performance. This may mean faster execution, lower memory usage or both. Not to be confused with mathematical optimization.

53 views

EvaluationMonitor slows down NDSolve considerably

Hi guys I'm solving a nonlinear system of ODEs with NDSolve. Since the dimension of the system ranges from 2700 to 20000 equations, depending on the parameters, the time required to solve the entire ...
88 views

NDSolve with default settings solves much faster than classic Runge-Kutta 4

NDSolve with default parameters takes 0.25 s for the first run. With Runge Kutta 4 specified, it takes about 4.6 s, ...
134 views

Summing matrix products

I need to compute a double sum over a weighted matrix product: $L[M]=\sum_{i,j}^{N}\Lambda[[i]]\;\omega[[i]].M.\omega^{\dagger}[[j]]$. $\Lambda$ is a list of with N complex values(weights) and ...
38 views

Is there a clean way to parallelize multi-index tables?

The documentation of ParallelTable indicates that if you want to parallelize the evaluation of a table of more than one dimension, such as ...
71 views

Improve recursive function (memoization)

These days I am trying to rewrite the following recursive function, in order to gain some speed. It is crucial because I end up using 4-5 similar functions, and I need to decrease execution time. ...
104 views

What are the main differences between RawArray and PackedArray?

What I know: PackedArray is documented (to some extent) in "Developer Utilities Package", RawArray is just mentioned in ...
67 views

Code optimizations with functions inside Module

I wrote a small code by using functions inside Module: ...
61 views

I have: ...
203 views

General solution for a linear ODE set with complicated coefficient

This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ...
177 views

How to turn off depth sorting of 3D curves for Manipulate?

Is there a way to turn off the default depth sorting of curves in a 3D output of several complicated curves ? Currently, I suspect that depth sorting has a very strong impact on performances on my ...
250 views

Complicated symbolic coefficient slows down equation solving

Here's a simple example for Solve: ...
152 views

How can I optimize the search between two lists, one that is changing length?

I'm trying to identify unique arrays by comparing two lists, one which is growing in length. The number of elements in the list grows as 2^n^2, where ...
185 views

Best approach for 'manual' common subexpression elimination

I have working code, but am looking for ways to make it more elegant. I have a fairly large expression with plenty of repetition and structure. A shortened toy example is ...
26 views

Smartest way to choose number of kernels? Which kernels are launched by LaunchKernels? [on hold]

Suppose you have something like below. hermMat is some hermitian matrix of dimensions {dim,dim} and ...
125 views

Lazy form of Tuples/Outer to loop over list of lists

This is less a question and more asking if someone has implemented this already, with more skill. I need to perform the Outer-like generalized outer product of a ...
63 views

Data acquisition from TCP socket

At last (since 10.3) we have straightforward/documented access to TCP sockets. It's been a long wait. So far there is very little discussion of the new feature. Although some older posts are still ...
32 views

Solving for limit of integration with a piecewise function (FindRoot vs NSolve) [duplicate]

I am trying to solve for the limits of integration using a piecewise function. I'm doing this in a loop over a list of data, mostly because I'm not well-versed enough in Mathematica to make this a ...
128 views

Indexing all elements of permutations $S_n$

I have this Table that gives all elements of $S_n$, I would like to know how to improve efficiency. ...
133 views

Why does Compile not make my function faster?

I need to speed up a large program that repeatedly calls the module below (I've not trimmed the code for this question to ensure there is enough calculation to show a speed improvement.) The obvious ...
242 views

Speed-up the computation of this sum of small matrices

Given a matrix mat with a large number of rows (a few thousands) and a few columns (between 2 and 10), I'd like to compute the sum of the "small" matrices obtained ...
263 views

Speed up RegionPlot

I want to plot a system of equalities and inequalities. I used a combination of ImplicitRegion and RegionPlot (since RegionPlot cannot plot lines or points). But this method is very slow than using ...
125 views

How to efficiently stream words and whitespace from a large text file

I want to tokenize a large (~20 MB) file, opening it and streaming the words, but preserving the whitespace as well. Example: ...
225 views

Primes Race (Mathematica Efficiency)

I am currently working with a paper that deals with this concept of Prime Races. You essentially create a large list of prime numbers and then split that list into two teams. You are assigned to ...
568 views

Improve speed in this tree - memoization won't suffice

I have two functions, one of which calls the other. I need to do some calculations but I was unable to optimize my code to do it efficiently. In search I came across the memoization technique, which ...
97 views

Counting runs in bits, along with their starts and lengths, in functional style

Here is some code to visualize Project Euler Problem 502. The code scans for runs of bits in the binary representation of an integer, and outputs the beginning position of each run and the length of ...
151 views

Problem with convergence of limiting value in Manipulate

I created a nice Manipulate box of the magnetic field outside and inside a spherical shell placed in an homogeneous magnetic field. The code is working great, but it has a problem at a limiting ...
84 views

efficient element wise multiplication of SparseArray vector and matrix

I have a large SparseArray $P$ of dimensions $\{d,d\}$ and I want to multiply a vector (also a SparseArray) $v$ of length $d$ ...
42 views

Prepending a sequence with zeros gives FindGeneratingFunction hard time

Asking for FindGeneratingFunction[{1, 3, 11, 43, 171, 683, 2731, 10923, 43691, 174763}, t] gives the answer (namely ...
408 views

Given a large binary matrix, find the largest submatrix containing non-zero elements

I'm looking for a way to reduce a binary matrix containing zeros at some positions into a matrix that contains no zeros by deleting rows and columns of the original matrix until only non-zero values ...
258 views

What is the fastest way to compute digits of $\pi$ using Mathematica?

There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ...
36 views

Customized ParallelTable - Automate ParallelSubmit - Possibly an issue with HoldAllComplete attribute

Related to this question and in particular its answer I am trying to wrap everything into a new parallelTab function that takes into account some cost per job, ...
98 views

Speed up Dynamic for graphical interface

I am trying to create a user interface where I can click on certain points in a set of data and save them into a list that can be used later in my code. The problem is it is currently sluggish. Is ...
166 views

Find the minimum positive-integer value which meet the requirement

If the equation is Mod[515 Sum[10^(3 d), {d, 0, n}], 53] == 0 Then I can get the minimum positive-integer value of n. ...
205 views

How to speed up calculation of this equation (FindRoot)

I have come up with the following functions, and I need to calculate a value, in order to have a condition valid. In my problem, all data are given, and I need to calculate variable l. I am using ...
115 views

How to optimize my own BezierFunction?

A few months ago, I asked a question about the implementation of Bezier surface. Please see here for a full detail. I also know that BezierFunction[] is built-in ...
222 views

Elegant way to partition list to be faster than ParallelTable (using ParallelSubmit), or some alternative?

Suppose you have a function fun[x_] := (Pause[.05*x]; x^2); of which you know that its evaluation time increases with its argument - in this case obviously ...
212 views

Error with FindMinimum. The Message is FindMinimum::cnpcons

I want to run a rather demanding check of feasibility. I have 3565 non-negativity constraints for my variables, and one that makes them sum to a certain budget they shall not surpass. I also have ...
167 views

Slow JoinAcross performance

Bug introduced in 10.3 I am using JoinAcross to combine two datasets, where the key is an Integer. ...
59 views

Speeding up ImageData[image,“Byte”]

For my image analysis I need the Byte values of many sequential 8bit PNG images. To obtain the Byte data I use: ...
280 views

Why is ListPlot[] so slow for coordinate pairs? Can we speed it up?

I compared the time it took to create a plot in two different ways. I expected the first method to be slower, but I was surprised at how much. Is this an inherent limitation or the function, or are ...
52 views

why URLFetch is slow when encapsulated by module and how to fix it [closed]

I'm using Mathematica 10.0.2 on Win7. I'm writing some program to crawl etymology of words on http://www.etymonline.com/. Below lies the example code: ...
113 views

Memory limit hit: optimize code for finding twin primes

I need some help optimizing a Mathematica code so that it'll not max out RAM. Here's the code: Cell 1 ...
35 views

Access variable middle of the run [duplicate]

I execute a Table[] that need large time to be finished. If I abort it I loose what evaluated until now. Does it possible to stop running and save what evaluated ...
96 views

How to improve speed of the following code

The following code do what I needed, but it takes too long ...
59 views

Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
195 views

How to efficiently find all combinations of the letters in an alphabet given a condition

Problem: I want to find all unique expressions with n number of terms that contain all the digits (or characters) in alphabet. ...
83 views

Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?

I've noticed that, while ListConvolve is very fast, it becomes much slower when you use anything but the standard Times,Plus as ...
149 views

Why is Random faster than RandomReal?

As of version 6, Random[] was superseded by RandomReal[ ] etc, but both still work perfectly well. Playing with some timing ...